## Photoacoustic image reconstruction from few-detector and limited-angle data |

Biomedical Optics Express, Vol. 2, Issue 9, pp. 2649-2654 (2011)

http://dx.doi.org/10.1364/BOE.2.002649

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### Abstract

Photoacoustic tomography (PAT) is an emerging non-invasive imaging technique with great potential for a wide range of biomedical imaging applications. However, the conventional PAT reconstruction algorithms often provide distorted images with strong artifacts in cases when the signals are collected from few measurements or over an aperture that does not enclose the object. In this work, we present a total-variation-minimization (TVM) enhanced iterative reconstruction algorithm that can provide excellent photoacoustic image reconstruction from few-detector and limited-angle data. The enhancement is confirmed and evaluated using several phantom experiments.

© 2011 OSA

## 1. Introduction

1. G. Paltauf, J. A. Viator, S. A. Prahl, and S. L. Jacques, “Iterative reconstruction algorithm for optoacoustic imaging,” J. Acoust. Soc. Am. **112**(4), 1536–1544 (2002). [CrossRef] [PubMed]

3. A. A. Oraevsky, A. A. Karabutov, S. V. Solomatin, E. V. Savateeva, V. A. Andreev, Z. Gatalica, H. Singh, and R. D. Fleming, “Laser optoacoustic imaging of breast cancer in vivo,” Proc. SPIE **4256**, 6–15 (2001). [CrossRef]

4. L. A. Kunyansky, “Explicit inversion formulae for the spherical mean radon transform,” Inverse Probl. **23**(1), 373–383 (2007). [CrossRef]

6. M. Xu and L. V. Wang, “Universal back-projection algorithm for photoacoustic computed tomography,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. **71**(1), 016706 (2005). [CrossRef] [PubMed]

7. Z. Yuan and H. Jiang, “Quantitative photoacoustic tomography: Recovery of optical absorption coefficient maps of heterogenous media,” Appl. Phys. Lett. **88**(23), 231101 (2006). [CrossRef]

8. L. Yin, Q. Wang, Q. Zhang, and H. Jiang, “Tomographic imaging of absolute optical absorption coefficient in turbid media using combined photoacoustic and diffusing light measurements,” Opt. Lett. **32**(17), 2556–2558 (2007). [CrossRef] [PubMed]

9. K. D. Paulsen and H. Jiang, “Spatially varying optical property reconstruction using a finite element diffusion equation approximation,” Med. Phys. **22**(6), 691–701 (1995). [CrossRef] [PubMed]

10. S. R. Arridge, “Forward and inverse problems in time-resolved infrared imaging,” in *Medical Optical Tomography: Functional Imaging and Monitoring*, G. J. Mueller, B. Chance, R. R. Alfano, S. B. Arridge, J. Beuthen, E. Gratton, M. Kaschke, B. R. Masters, S. Svanberg, and P. van der Zee, eds. (SPIE Press, 1993), pp. 35–64.

11. S. J. LaRoque, E. Y. Sidky, and X. Pan, “Accurate image reconstruction from few-views and limited-angle data in diffraction tomography,” J. Opt. Soc. Am. A **25**(7), 1772–1782 (2008). [CrossRef]

12. J. Bian, J. H. Siewerdsen, X. Han, E. Y. Sidky, J. L. Prince, C. A. Pelizzari, and X. Pan, “Evaluation of sparse-view reconstruction from flat-panel-detector cone-beam CT,” Phys. Med. Biol. **55**(22), 6575–6599 (2010). [CrossRef] [PubMed]

16. K. Wang, E. Y. Sidky, M. A. Anastasio, A. A. Oraevsky, and X. Pan, “Limited data image reconstruction in optoacoustic tomography by constrained total variation minimization,” Proc. SPIE **7899**, 78993U, 78993U-6 (2011). [CrossRef]

## 2. Method

17. L. Yao and H. Jiang, “Finite-element-based photoacoustic tomography in time-domain,” J. Opt. A, Pure Appl. Opt. **11**(8), 085301 (2009). [CrossRef]

*p*is the pressure wave;

*β*is the thermal expansion coefficient;

*λ*is the regularization parameter determined by combined Marquardt and Tikhonov regularization schemes; and

**I**is the identity matrix.

18. K. D. Paulsen and H. Jiang, “Enhanced frequency-domain optical image reconstruction in tissues through total-variation minimization,” Appl. Opt. **35**(19), 3447–3458 (1996). [CrossRef] [PubMed]

*δ*are typically positive parameters that need to be determined numerically. The minimization of Eq. (4) can be realized by the differentiation of

18. K. D. Paulsen and H. Jiang, “Enhanced frequency-domain optical image reconstruction in tissues through total-variation minimization,” Appl. Opt. **35**(19), 3447–3458 (1996). [CrossRef] [PubMed]

*V*is formed by

*R*is formed by

*R*and the construction of column vector

*V*.

## 3. Results

20. Z. Wang and A. C. Bovik, “A universal image quality index,” IEEE Signal Process. Lett. **9**(3), 81–84 (2002). [CrossRef]

*j*= 0 and 1. UQI measures the image similarity between the reconstructed (

## 4. Conclusions

## Acknowledgment

## References and links

1. | G. Paltauf, J. A. Viator, S. A. Prahl, and S. L. Jacques, “Iterative reconstruction algorithm for optoacoustic imaging,” J. Acoust. Soc. Am. |

2. | S. J. Norton and T. Vo-Dinh, “Optoacoustic diffraction tomography: analysis of algorithms,” J. Opt. Soc. Am. A |

3. | A. A. Oraevsky, A. A. Karabutov, S. V. Solomatin, E. V. Savateeva, V. A. Andreev, Z. Gatalica, H. Singh, and R. D. Fleming, “Laser optoacoustic imaging of breast cancer in vivo,” Proc. SPIE |

4. | L. A. Kunyansky, “Explicit inversion formulae for the spherical mean radon transform,” Inverse Probl. |

5. | D. Finch, S. Patch, and Rakesh, “Determining a Function from Its Mean Values Over a Family of Spheres,” SIAM J. Math. Anal. |

6. | M. Xu and L. V. Wang, “Universal back-projection algorithm for photoacoustic computed tomography,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. |

7. | Z. Yuan and H. Jiang, “Quantitative photoacoustic tomography: Recovery of optical absorption coefficient maps of heterogenous media,” Appl. Phys. Lett. |

8. | L. Yin, Q. Wang, Q. Zhang, and H. Jiang, “Tomographic imaging of absolute optical absorption coefficient in turbid media using combined photoacoustic and diffusing light measurements,” Opt. Lett. |

9. | K. D. Paulsen and H. Jiang, “Spatially varying optical property reconstruction using a finite element diffusion equation approximation,” Med. Phys. |

10. | S. R. Arridge, “Forward and inverse problems in time-resolved infrared imaging,” in |

11. | S. J. LaRoque, E. Y. Sidky, and X. Pan, “Accurate image reconstruction from few-views and limited-angle data in diffraction tomography,” J. Opt. Soc. Am. A |

12. | J. Bian, J. H. Siewerdsen, X. Han, E. Y. Sidky, J. L. Prince, C. A. Pelizzari, and X. Pan, “Evaluation of sparse-view reconstruction from flat-panel-detector cone-beam CT,” Phys. Med. Biol. |

13. | H. Ammari, E. Bretin, V. Jugnon, and A. Wahab, “Photo-acoustic imaging for attenuating acoustic media,” in |

14. | H. Ammari, E. Bossy, V. Jugnon, and H. Kang, “Mathematical models in photoacoustic imaging of small absorbers,” SIAM Rev. |

15. | H. Ammari, E. Bossy, V. Jugnon, and H. Kang, “Reconstruction of the optical absorption coefficient of a small absorber from the absorbed energy density,” SIAM J. Appl. Math. |

16. | K. Wang, E. Y. Sidky, M. A. Anastasio, A. A. Oraevsky, and X. Pan, “Limited data image reconstruction in optoacoustic tomography by constrained total variation minimization,” Proc. SPIE |

17. | L. Yao and H. Jiang, “Finite-element-based photoacoustic tomography in time-domain,” J. Opt. A, Pure Appl. Opt. |

18. | K. D. Paulsen and H. Jiang, “Enhanced frequency-domain optical image reconstruction in tissues through total-variation minimization,” Appl. Opt. |

19. | H. Jiang, Z. Yuan, and X. Gu, “Spatially varying optical and acoustic property reconstruction using finite-element-based photoacoustic tomography,” J. Opt. Soc. Am. A |

20. | Z. Wang and A. C. Bovik, “A universal image quality index,” IEEE Signal Process. Lett. |

**OCIS Codes**

(100.2980) Image processing : Image enhancement

(170.3010) Medical optics and biotechnology : Image reconstruction techniques

(170.5120) Medical optics and biotechnology : Photoacoustic imaging

(170.6960) Medical optics and biotechnology : Tomography

**ToC Category:**

Photoacoustic Imaging and Spectroscopy

**History**

Original Manuscript: July 22, 2011

Revised Manuscript: August 19, 2011

Manuscript Accepted: August 19, 2011

Published: August 19, 2011

**Citation**

Lei Yao and Huabei Jiang, "Photoacoustic image reconstruction from few-detector and limited-angle data," Biomed. Opt. Express **2**, 2649-2654 (2011)

http://www.opticsinfobase.org/boe/abstract.cfm?URI=boe-2-9-2649

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### References

- G. Paltauf, J. A. Viator, S. A. Prahl, and S. L. Jacques, “Iterative reconstruction algorithm for optoacoustic imaging,” J. Acoust. Soc. Am.112(4), 1536–1544 (2002). [CrossRef] [PubMed]
- S. J. Norton and T. Vo-Dinh, “Optoacoustic diffraction tomography: analysis of algorithms,” J. Opt. Soc. Am. A20(10), 1859–1866 (2003). [CrossRef] [PubMed]
- A. A. Oraevsky, A. A. Karabutov, S. V. Solomatin, E. V. Savateeva, V. A. Andreev, Z. Gatalica, H. Singh, and R. D. Fleming, “Laser optoacoustic imaging of breast cancer in vivo,” Proc. SPIE4256, 6–15 (2001). [CrossRef]
- L. A. Kunyansky, “Explicit inversion formulae for the spherical mean radon transform,” Inverse Probl.23(1), 373–383 (2007). [CrossRef]
- D. Finch, S. Patch, and Rakesh, “Determining a Function from Its Mean Values Over a Family of Spheres,” SIAM J. Math. Anal.35(5), 1213–1240 (2004). [CrossRef]
- M. Xu and L. V. Wang, “Universal back-projection algorithm for photoacoustic computed tomography,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys.71(1), 016706 (2005). [CrossRef] [PubMed]
- Z. Yuan and H. Jiang, “Quantitative photoacoustic tomography: Recovery of optical absorption coefficient maps of heterogenous media,” Appl. Phys. Lett.88(23), 231101 (2006). [CrossRef]
- L. Yin, Q. Wang, Q. Zhang, and H. Jiang, “Tomographic imaging of absolute optical absorption coefficient in turbid media using combined photoacoustic and diffusing light measurements,” Opt. Lett.32(17), 2556–2558 (2007). [CrossRef] [PubMed]
- K. D. Paulsen and H. Jiang, “Spatially varying optical property reconstruction using a finite element diffusion equation approximation,” Med. Phys.22(6), 691–701 (1995). [CrossRef] [PubMed]
- S. R. Arridge, “Forward and inverse problems in time-resolved infrared imaging,” in Medical Optical Tomography: Functional Imaging and Monitoring, G. J. Mueller, B. Chance, R. R. Alfano, S. B. Arridge, J. Beuthen, E. Gratton, M. Kaschke, B. R. Masters, S. Svanberg, and P. van der Zee, eds. (SPIE Press, 1993), pp. 35–64.
- S. J. LaRoque, E. Y. Sidky, and X. Pan, “Accurate image reconstruction from few-views and limited-angle data in diffraction tomography,” J. Opt. Soc. Am. A25(7), 1772–1782 (2008). [CrossRef]
- J. Bian, J. H. Siewerdsen, X. Han, E. Y. Sidky, J. L. Prince, C. A. Pelizzari, and X. Pan, “Evaluation of sparse-view reconstruction from flat-panel-detector cone-beam CT,” Phys. Med. Biol.55(22), 6575–6599 (2010). [CrossRef] [PubMed]
- H. Ammari, E. Bretin, V. Jugnon, and A. Wahab, “Photo-acoustic imaging for attenuating acoustic media,” in Mathematical Modeling in Biomedical Imaging II, H. Ammari, ed., Vol. 2035 of Lecture Notes in Mathematics (Springer, 2011), pp. 53–80.
- H. Ammari, E. Bossy, V. Jugnon, and H. Kang, “Mathematical models in photoacoustic imaging of small absorbers,” SIAM Rev.52(4), 677–695 (2010). [CrossRef]
- H. Ammari, E. Bossy, V. Jugnon, and H. Kang, “Reconstruction of the optical absorption coefficient of a small absorber from the absorbed energy density,” SIAM J. Appl. Math.71, 676–693 (2011). [CrossRef]
- K. Wang, E. Y. Sidky, M. A. Anastasio, A. A. Oraevsky, and X. Pan, “Limited data image reconstruction in optoacoustic tomography by constrained total variation minimization,” Proc. SPIE7899, 78993U, 78993U-6 (2011). [CrossRef]
- L. Yao and H. Jiang, “Finite-element-based photoacoustic tomography in time-domain,” J. Opt. A, Pure Appl. Opt.11(8), 085301 (2009). [CrossRef]
- K. D. Paulsen and H. Jiang, “Enhanced frequency-domain optical image reconstruction in tissues through total-variation minimization,” Appl. Opt.35(19), 3447–3458 (1996). [CrossRef] [PubMed]
- H. Jiang, Z. Yuan, and X. Gu, “Spatially varying optical and acoustic property reconstruction using finite-element-based photoacoustic tomography,” J. Opt. Soc. Am. A23(4), 878–888 (2006). [CrossRef] [PubMed]
- Z. Wang and A. C. Bovik, “A universal image quality index,” IEEE Signal Process. Lett.9(3), 81–84 (2002). [CrossRef]

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